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Determining the impulse characteristic of a stable linear element. (English. Russian original) Zbl 0696.93020

Sov. Phys., Dokl. 34, No. 2, 89-90 (1989); translation from Dokl. Akad. Nauk SSSR 304, No. 6, 1312-1314 (1989).
For a stable linear element described by \(z(t)=\int^{t}_{0}K(s)u(t- s)ds\), where K(t) is the impulse response and z(t) is the output, the input \(u(t)=\sin (at^ 2+bt)\), \(t\geq 0\), is considered (a,b being suitable constants). It is shown that, under certain conditions, \(H(t;a)=(4a/\pi)\int^{\infty}_{0}z(\tau)\sin [a(\tau -t)^ 2+b(\tau -t)]d\tau\) is an estimate of K(t), i.e. \(\lim_{a\to \infty}| H(t;a)-K(t)| =0\) uniformly on each finite time interval. Similar results are obtained for the cases when the excitation/observation time is finite and/or z(t) is unavoidable altered by measuring errors.
Reviewer: M.Voicu

MSC:

93B30 System identification
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
44A35 Convolution as an integral transform
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